Finding points of intersection between two symbolic functions

Hi,

I am in the middle of trying to find the points of intersection between two symbolic functions.

The two equations are defined as follows

syms x y f;

lhs  = 1.425*y^2 - 13.4798*x^2 + 0.85*sqrt((-2.353*y^2 - x^2)*(y^2 + x^2))*cot(1e-7*(sqrt((-2.353*y^2 - x^2))))

f = 2.833653982*x - 0.2403942747e10

Now, since the point of intersection has the same (x,y) coordinates for both curves, substitution should simply work.

So I now run

lhs_solve = subs(lhs, y, f)

S  = solve(lhs_solve, x)

This produces a complex output, indicating there is no point of intersection. However, graphically the equations definitely cross!

Has anybody experienced this problem before? And is there any way to bypass this?

Thanks,

Carl